Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems

Stéphane Junca (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We study the propagation of high frequency oscillations for one dimensional semi-linear hyperbolic systems with small parabolic perturbations. We obtain a new degenerate parabolic system for the profile, and valid an asymptotic development in the spirit of Joly, Métivier and Rauch.

Mots clés: BKW; vanishibg viscosity

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Junca. Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems. Revista Matemática Iberoamericana, 2008, 24 (2), pp.549-566. ⟨10.4171/RMI/546⟩. ⟨hal-01145732⟩